I have faced some problem in computing surface integral of some vectors in spherical polar coordinate system I have studied that in genaral infinitesimal surface differential vector has three component along $r$, $θ$ and $\phi$ cap direction
$$ds=r^2\sinθ\mathrm dθ\mathrm d\phi r' + r\sinθ\mathrm dr\mathrm d\phi θ' + r\mathrm dr\mathrm dθ\phi'$$ Where $r',\phi',θ'$ are the unit vectors So suppose I have a vector $$ v=Ar'+bθ' $$ And I want to calculate
$$∮v.\mathrm ds.$$ over a spherical surface
Then on which surface components do I have to integrate ?? I mean on spherical surface only there radius is constant so $\mathrm dr=0$ ! But my problem is then what are actually the other surface components are here? I mean if it be a solid sphere then it might have all three surface differential components then how can I understand all surface differential components, only the surface i understand is the normal to the outer surface which is along the $r'$.
Can you show me the other components with picture?